The attached picture is of one of the four 'Eteila' cards from an unidentified 'Etteila' related deck at the British Museum.

Following inquiries by myself to Thierry Depaulis, Phillipa Plock & the Waddeson Manor curators, the deck at the British Museum has now been positively identified as being the same as:

Le Nouvel Eteila, ou Petit necromancien. Le Petit Oracle des Dames
Primary Maker unknown
Secondary Maker: Mme. Finet. Rue de l’Arbre-sec, No.26, Paris
First definite notice we have of it is in 1820, from 'Robert' from the same address (Rue de l’Arbre-sec, No. 26, Paris)
There is a later note of Mme. Finet, 1824

However, the design and engraving has been variously dated as being late 18th or early 19th century - if so, some connection with Jacques Grasset de Saint-Sauveur is considered possible. Noting especially that both this deck and the Saint-Sauveur PODD draw elements from the c.1790 "Jeu divinatoire révolutionnaire".

A copy of the deck (as an uncut sheet) is in the Rothschild Collection, as Cataloged by Phillipa Plock (Waddesdon Manor – Printed Board Games Collection, August 2009).

Nouvelle Eteila, ou le petit Nécromancien, Le petit oracle des dames

Divinatory card game with standard piquet pack and four extra cards derived from the Tarot of Etteilla (Jean-Baptiste Alliette). The sheet is divided into 36 rectangles arranged in rows with smaller reserves for the suits on the right-hand side. At lower right, there is a blank reserve for the shop name to be written in. The image is etched and hand-coloured, the text is engraved.

This is a sheet of fortune telling cards using some of the imagery devised by Etteilla. The pack here is a standard French piquet pack of 32 cards Ace, King, Queen, Jack, 10, 9, 8, 7, of the usual four French suits but with four extra Ettellia cards. Decker, Depaulis and Dummett (1996) refer to a 36 card pack produced by Madame Finet in about 1800 under the title “le Petit Oracle des Dames”, which is the same game.

Depaulis (correspondence 18 June 2009) now dates the game slightly later, circa 1810, and notes that there are suit signs. The game was included in the exhibition of 1989 “Les cartes de la Révolution”, with the earlier date. Depaulis notes that the game draws on another, earlier and somewhat mysterious set of cards, which he called “Jeu politico-divinatoire” (n° 99 in the 1989 “Les cartes de la Révolution” catalogue), which is in the BnF and bears the APR (“Avec Privilège du Roi”) imprint so it must date from around 1790. A very similar game was produced circa 1810 by Robert, see Decker, Depaulis and Dummett (1996). There are copies of Mme Finet’s sheet in the Cary collection of playing cards (Yale University Library). They are catalogued as FRA 194 and FRA sheet 176. I am grateful to Thierry Depaulis for this information.

Thierry Depaulis (correspondence 19th December, 2015) now considers that the original design and engravings appear to be earlier, c. late 18th century. But notes that the only dates we positively have are 1820 (re: Robert) and 1824 (re: Mme. Finet).

Ronald Decker,Thierry Depaulis and Michael Dummett,’’A Wicked Pack of Cards: The Origins of the Occult Tarot’’, New York, 1996; p. 143; discusses another copy of the game.

William B. Keller, ‘‘A catalogue of the Cary collection of playing cards in the Yale University Library’’, New Haven, 1981; discusses another copy of the game

The game is also cataloged in "Le cabinet des estampes de la Bibliothèque nationale : guide du lecteur et du visiteur, catalogue général et raisonné des collections qui y sont conservées", by Bouchot, Henri, 1849-1906. However, I find no record of it in the current Bibliotheque nationale Francaise online database.

Another copy of the game was sold from a private collection, 2009, at auction. (est.price 300-450 Euros, final price 700 Euros).